How do I separate 1 Vertex that has 2 UVs?
A vertex exists in five-dimensional space, with coordinates (x,y,z,u,v), so while two vertices may share coordinates in 3D space, they can still be in different places in UV space.

Every time you create a UV seam, or have two different shading groups (flat shading), under the hood you are splitting those vertices along the seam into multiple vertices. It's confusing though because Blender will still treat these as a single vertex in many circumstances.

The way you can get around with for UV editing is to turn off UV Sync Selection:


The down-side is that only elements of your mesh that you've got selected in 3D view will show up in UV view, but this will allow you to manipulate vertices separately in the UV editor, even if they appear to be the same vertex in the 3D view.